Rajae Aboulaich

New diffusion models in image processing

We give some diffusion models which can be used for restoration in image processing. The proposed model is a combination of fast growth with respect to low gradient and slow growth when the gradient is large. The existence theorem for solutions and some numerical results are given.

A new hybrid method for solving global optimization problem

Abstract In this paper we present a new hybrid method, called the SASP method. The purpose of this method is the hybridization of the simulated annealing (SA) with the descent method, where we estimate the gradient using simultaneous perturbation. Firstly, the new hybrid method finds a local minimum using the descent method, then SA is executed in order to escape from the currently discovered local minimum to a better one, from which the descent method restarts a new local search, and so on until convergence. The new hybrid method can be widely applied to a class of global optimization problems for continuous functions with constraints. Experiments on 30 benchmark functions, including high dimensional functions, show that the new method is able to find near optimal solutions efficiently. In addition, its performance as a viable optimization method is demonstrated by comparing it with other existing algorithms. Numerical results improve the robustness and efficiency of the method presented.

Shape optimization for a simulation of a semiconductor problem

This work gives a study of the Regier’s model by using the shape optimization techniques. Two formulations of this model are proposed with appropriate boundary conditions of the MESFET transistor. In each formulation the existence of a free boundary, separating the depletion and neutrality of charge regions, is proved with some hypothesis. The shape gradient is calculated for each formulation to approach the solution. To approximate the free boundary, two algorithms are presented. Numerical results obtained by implementing the last algorithm prove that this shape optimization techniques provide a reasonably smooth free boundary.

Quasi‐variational inequality and shape optimization for solution of a free boundary problem

Electrical potentials in a junction field transistor can be calculated using a simplified model based on a complete depletion assumption. This gives rise to a free boundary problem. We show here how we can approximate this problem with a quasi‐variational inequality technique and the shape optimization method. A detailed analysis of these methods is presented. Using some numerical experiments we compare our results with the solution of the discrete drift‐diffusion system, accomplished with a Gummel‐like algorithm. The numerical results suggest that the methods proposed here work successfully and that the shape optimization technique provides a reasonably free boundary without excessive iterations.

Numerical approach of a free boundary in the junction field effect transistor — MESFET

This paper presents the numerical approach of the free boundary by using shape optimization method. The numerical simulation field effect transistor MESFET is possible with the Laplace–Poisson model, which introduces two regions, respectively, known by “charge neutrality region” and “depletion region”, separated by some free boundary.

Modeling Consumers’ Behavior in New Dual Banking Markets: The Case of Morocco

This paper aims to model the impact of retail consumers’ behavior on a new banking dual market featuring both conventional and Islamic banking products. To build the model, we conduct an empirical qualitative and quantitative survey on Moroccan market consumers in order to appraise their preferences with regard to banking products’ attributes. Then, we use conjoint analysis method to determine the consumers’ decision function. We run market simulations on a Multi-Agents Simulation platform and analyze the results. Our findings indicate that in new dual markets, and under a range of assumptions, it is predicted that Islamic banks will face excess liquidity while conventional banks will be exposed to liquidity shortage.

Impact of Qualitative Characteristics on Market Equilibrium. Simulation with Agent-Based Modeling

This paper involves developing financial utility function that considers compliance to a certain qualitative characteristic and studies the impact on market equilibrium prices, should this criterion be Sharia compliance, fair-trade, environmental, social and governance principles or other ethical aspect. The goal is to show that individual utility can depend on other parameters than wealth and risk aversion, that therefore influence equilibrium market prices. This has been done by examining a possible utility function that takes into account individual sensitivity to the criterion and the intrinsic quality of compliance of this parameter. In order to prove the effectiveness of the proposed utility function, a simulation is made using agent-based approach with NetLogo platform. Upon examination of the impact of these parameters, it becomes clear that compliance to a qualitative characteristic would impact individual utility, supply and demand and result in equilibrium prices. This research highlights the importance of ethical arguments on individual decision making and how markets behave to this.

Improving Capital Budgeting Through Probabilistic Approaches

This article advocates the multiple benefits of applying probabilistic approaches to capital budgeting through enriching the deterministic framework with a stochastic modeling of main impacting inputs (including a methodology for selecting the most important inputs to be modeled stochastically). The essential limitations of the deterministic capital budgeting methodology are presented: behavioral biases (optimism, asymmetric probability distribution, etc.), incomplete view of the risk return profile, neglecting real options (be it to evaluate a project or to reshape it in a value creation perspective), portfolio diversification impact, etc. Through some selected examples, we illustrate how each of these limitations can be mitigated thanks to probabilistic approaches leading to a better decision-making process and ultimately more value creation.